First, download the full Oracle Database Client package that matches the version of your Oracle database. If your machine is 64-bit, download the 64-bit package. Note: you must download the full client, not the "Instant Client."
Unzip the package and run the setup program with administrator privileges. Choose 'Custom' installation.
A few screens will follow. Choose the language of installation. When it asks what account you want services to run under, just choose "Windows Built-in Account," since we won't be installing any services anyway.
It will ask you where you want your "Oracle Base" directory to be. You can see what I chose in the following screenshot. The "Oracle Home" location field should automatically set itself according to what you choose for your Oracle base directory. I recommend not messing with the software location; just stick with the default.
On the next screen we choose what components to install. Choose "Oracle Database Utilities," "SQL*Plus," and "Oracle Net."
Finish the remaining screens to complete the installation. SQLplus and rman should now be available to you on your path and command line.
Before you can use sqlplus to connect to your database, you must create and configure a tnsnames.ora file. That is outside the scope of this question, but once the file is created, it should be placed in its default location, which is
<<ORACLE_HOME>>\network\admin folder. If you cannot determine the location of your
<<ORACLE_HOME>> folder, you can find it in your Windows registry at [HKEY_LOCAL_MACHINE\SOFTWARE\Oracle\KEY_OraClient12Home1] in a string value called ORACLE_HOME.
You should now be able to open a command prompt and type sqlplus username@oraclesid (where oraclesid is the sid of your Oracle database as specified in your tnsnames.ora file) and connect from your workstation. rman should work from the command line as well.